\(P=1+\left(\dfrac{2a+\sqrt{a}-1}{1-a}-\dfrac{2a\sqrt{a}-\sqrt{a}+a}{1-a\sqrt{a}}\right)\left(\dfrac{a-\sqrt{a}}{2\sqrt{a}-1}\right)\)
\(=1+\left[\dfrac{\sqrt{a}\left(\sqrt{a}+1\right)\left(2\sqrt{a}-1\right)}{\left(\sqrt{a}-1\right)\left(\sqrt{a}+a+1\right)}-\dfrac{\left(\sqrt{a}+1\right)\left(2\sqrt{a}-1\right)}{\left(\sqrt{a}+1\right)\left(\sqrt{a}-1\right)}\right]\)\(\times\dfrac{\sqrt{a}\left(\sqrt{a}-1\right)}{2\sqrt{a}-1}\)
\(=1+\left(\dfrac{a\left(\sqrt{a}+1\right)}{\sqrt{a}+a+1}-\sqrt{a}\right)\)
\(=\dfrac{\sqrt{a}+a+1+a\sqrt{a}+a-a-a\sqrt{a}-\sqrt{a}}{a+\sqrt{a}+1}\)
\(=\dfrac{a+1}{a+\sqrt{a}+1}\)
(^~^)
\(\dfrac{a+1}{a+\sqrt{a}+1}=\dfrac{\sqrt{6}}{1+\sqrt{6}}\)
<=> \(a+\sqrt{6}a+1+\sqrt{6}=\sqrt{6}a+\sqrt{6a}+\sqrt{6}\)
<=> \(a-\sqrt{6a}+1=0\left(1\right)\)
<=> \(\left(\sqrt{a}-\sqrt{2+\sqrt{3}}\right)\left(\sqrt{a}-\sqrt{2-\sqrt{3}}\right)=0\)
<=> \(\left[{}\begin{matrix}a=2+\sqrt{3}\\a=2-\sqrt{3}\end{matrix}\right.\)
